David Allen, who has died aged 78, was an extremely accomplished cricketer, both for Gloucestershire and for England. A shrewd offspin bowler who maintained a tight line, with the subtlest of variations, he was also a determined lower-order batsman, and it was in this role that his most dramatic moment came.

The Lord's Test match of 1963 culminated in the West Indies fast bowler Wes Hall storming in for the final over with England nine wickets down and needing six runs to win. The England master batsman Colin Cowdrey returned to the crease with his recently broken forearm in plaster. He walked to the non-striker's end and would not necessarily have to face the bowling. But though Cowdrey emerged from the contest a hero, the man who really saved England, the batsman on strike as Hall roared in, was Allen: it was he who resolutely saw England to the draw.

Throughout the 1960s, following the retirement of the great Jim Laker, English cricket was well supplied with offspinners, yet Allen earned 39 Test caps, playing against all the other Test-playing nations of the time. In 1963 he found himself one of three offspinners sharing in the attack at Sydney, in the final Test against Australia, with fellow operators Fred Titmus and Ray Illingworth.

It was an offspinners' world in county cricket too, not least at Gloucestershire, where two or three frontline off-break merchants – Bryan "Bomber" Wells, John Mortimore and Allen, far from identical in method – were fielded regularly. Not surprisingly, the club's home pitches were usually sympathetic to this type of bowling. Allen's career-best figures came away from the main ground in Bristol, at Lydney, with 8 for 34 against Sussex in 1969.

His sole century, 121 not out, came against Nottinghamshire at Trent Bridge in 1961, and pointed to what a batsman he might have been had he not been slotted lower in the order in the specialist offspinner's role. His Test batting average of 25.50 (five 50s, highest 88 v New Zealand at Christchurch in 1965-66) also revealed a deeper potential.

Allen took 122 wickets for England at 30.97, conceding only two runs per over. His best Test figures were 5 for 30 against Pakistan at Dhaka on England's 1961-62 tour of the subcontinent, an attritional campaign, with Allen dropping on a tight length through a challenging 482.3 overs in eight Tests against Pakistan and India, taking 34 wickets at 27 apiece.

In his Test debut, in Barbados in 1960, he ran out Easton McMorris with his first touch of the ball as West Indies set about their reply to England's 482. Soon Garfield Sobers and Frank Worrell were embarking on their record stand of 399 in little short of 10 hours. Allen showed his mettle with 0 for 82 off 43 overs.

One memorable performance for England with a particularly unhappy outcome was his spell against Australia at Old Trafford in 1961, which had the enemy on the run in the third innings of the match. He had dismissed Bill Lawry, Ken Mackay, Richie Benaud and Wally Grout, leaving Australia only 157 ahead with one wicket remaining. Alan Davidson then thumped Allen for 20 in one over, and Peter May withdrew him from the attack. The Davidson/Graham McKenzie last-wicket stand roared on to 98, leaving England with a target of 256. With Benaud bowling leg-spin around the wicket into the rough, Australia pulled off an improbable 54-run victory to retain the Ashes. Allen was left to contemplate a bowling analysis that was certainly impressive as far as it went: 38 overs, 25 maidens, four wickets for 58.

His short and effortless run-up took little out of him, which was just as well when, a year later, he toured Australia for the first time and had to labour for wickets. Still, he returned in 1965-66, and at least kept things tight: his reliability was universally admired.

Allen was born in Horfield, Bristol, and educated at Cotham grammar school. His early cricket was with the Stapleton and Almondsbury clubs. Starting in 1953, when only 17 (he took 6 for 13 to beat the mighty Surrey team), he scored 7,510 runs for his county (average 18.58), taking 882 wickets (22.12), and attaining the double of 1,000 runs and 100 wickets in 1961.

His last Test came in 1966, and in his final county seasons, relations with his captain, Tony Brown, with whom he had come through the ranks, became somewhat strained. At the end of his time as a player with Gloucestershire, in 1972, Allen even found himself left out of his benefit match. After cricket, he worked as an area manager for the wine merchants Harvey's and then Allied Domecq. He became the county club's president in 2011, serving with customary geniality, and was also president of Thornbury cricket club.

Allen is survived by his wife, Joyce (nee Pearce), son, Mark, daughter, Tracey, four granddaughters and a grandson.

• David Arthur Allen, cricketer, born 29 October 1935; died 24 May 2014

• This article was amended on 28 May 2014. Peter May, and not Ted Dexter, captained England in the Old Trafford Test of 1961.